Whisk together the 3 tablespoons balsamic vinegar, 6 tablespoons olive oil, Dijon, garlic, shallot, salt, and pepper. Place steak in a zip-top bag, pour balsamic mixture over, seal tightly, and refrigerate, 8 hours or overnight.
Heat grill and add marinated steak. Grill each side of the steak for 5 minutes, turning 90 degrees after 2 1/2 minutes to create a diamond mark on the steak. Remove from grill once internal temperature reaches 140 degrees F (60 degrees C). Brush with 3 teaspoons balsamic vinegar, season with salt, then cover and let rest for 10 minutes.
While steak is resting, grate cheese and slice cherry tomatoes in half. Cut the steak into thin slices and serve over a bed of arugula. Garnish with cherry tomatoes, cheese, a drizzle of extra-virgin olive oil, and freshly cracked pepper.
